The parabola
Not so obvious is the point which moves so that its distance from a point (the
focus F) is the same as its perpendicular distance from a given line (the directrix).
In this case we get a parabola. The parabola has a host of useful properties. If a
light source is placed at the focus F, the emitted light rays are all parallel to PM.
On the other hand, if TV signals are sent out by a satellite and hit a parabola-
shaped receiving dish, they are gathered together at the focus and are fed into
the TV set.
If a stick is rotated about a point any fixed point on the stick traces out a
circle, but if a point is allowed to moved outwards along the stick in addition to it
being rotated this generates a spiral. Pythagoras loved the spiral and much later
Leonardo da Vinci spent ten years of his life studying their different types, while
René Descartes wrote a treatise on them. The logarithmic spiral is also called the
equiangular spiral because it makes the same angle with a radius and the tangent
at the point where the radius meets the spiral.
marcin
(Marcin)
#1